A256929 Decimal expansion of Sum_{k>=1} (zeta(2k)/k)*(1/3)^(2k).

1, 0, 5, 0, 0, 9, 1, 1, 5, 0, 0, 9, 4, 8, 2, 2, 1, 0, 0, 1, 7, 5, 7, 9, 1, 6, 9, 1, 6, 5, 7, 9, 3, 8, 5, 9, 5, 3, 4, 0, 4, 4, 6, 1, 1, 3, 7, 4, 9, 2, 8, 6, 9, 0, 3, 3, 2, 6, 0, 3, 0, 5, 7, 2, 3, 2, 0, 4, 7, 3, 3, 6, 9, 3, 0, 2, 8, 4, 0, 0, 6, 3, 7, 4, 8, 2, 8, 2, 7, 9, 7, 8, 0, 8, 6, 1, 6, 7, 6, 3, 8, 9, 0

Offset

0,3

References

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 272.

Links

Table of n, a(n) for n=0..102.

Eric Weisstein's MathWorld, Riemann Zeta Function

Wikipedia, Riemann Zeta Function

Formula

Equals log(Gamma(3/4)*Gamma(5/4)) = log(A068465*A068467).

Equals log(Pi/(2*sqrt(2))) = log(A093954).

Equals -Sum_{k>=1} log(1 - 1/(4*k)^2). - Amiram Eldar, Aug 12 2020

Example

0.1050091150094822100175791691657938595340446113749286903326...

Mathematica

RealDigits[Log[Pi/(2*Sqrt[2])], 10, 103] // First

Crossrefs

Cf. A068465, A068467, A093954, A256930.

Sequence in context: A308224 A200630 A198225 * A068459 A099222 A341796

Adjacent sequences: A256926 A256927 A256928 * A256930 A256931 A256932

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 13 2015

Status

approved